Eulerian limit for 2D Navier-Stokes equation and damped/driven KdV equation as its model

We discuss the inviscid limits for the randomly forced 2D Navier-Stokes equation (NSE) and the damped/driven KdV equation. The former describes the space-periodic 2D turbulence in terms of a special class of solutions for the free Euler equation, and we view the latter as its model. We review and revise recent results on the inviscid limit for the perturbed KdV and use them to suggest a setup which could be used to make a next step in the study of the inviscid limit of 2D NSE. The proposed approach is based on an ergodic hypothesis for the flow of the 2D Euler equation on iso-integral surfaces. It invokes a Whitham equation for the 2D Navier-Stokes equation, written in terms of the ergodic measures. Dedicated to Vladimir Igorevich Arnold on his 70th birthday     

Entanglement of qutrits

For two types of qutrits specified by the dynamical symmetry SU(3) and SU(2), we consider the difference in entanglement caused by the lack of quantum observables in the latter case. In particular, we show that the SU(2) qutrits can have specific separable entanglement caused by quantum correlations of intrinsic degrees of freedom in a single party without interparty correlations.     

Trends in sorption preconcentration combined with noble metal determination.

Nowadays much attention is being paid to the determination of trace amounts of noble metals in geological, industrial, biological and environmental samples. The most promising techniques, such as inductively coupled plasma atomic emission spectrometry (ICP-AES), inductively coupled plasma mass spectrometry (ICP-MS) and electrothermal atomic absorption spectrometry (ETAAS) are characterized by high sensitivity. However, the accurate determination of trace noble metals has been limited by numerous interferences generated from the presence of matrix elements. To decrease, or eliminate, these interferences, the sorption preconcentration of noble metals is often used prior to their instrumental detection. A great number of hyphenated methods of noble metal determination using sorption preconcentration have been developed. This review describes the basic types of available sorbents, preconcentration procedures and preparations of the sorbent to the subsequent determination of noble metals. The specific features of instrumental techniques and examples of ETAAS, FAAS, ICP-AES, ICP-MS determinations after the sorption preconcentration of noble metals are considered. The references cited here were selected mostly from the period 1996 - 2006.     

III-V compound semiconductor (001) surfaces

There has been renewed interest in the structure of III-V compound semiconductor (001) surfaces caused by recent experimental and theoretical findings, which indicate that geometries different from the seemingly well-established dimer models describe the surface ground state for specific preparation conditions. I review briefly the structure information available on the (001) surfaces of GaP, InP, GaAs and InAs. These data are complemented with first-principles total-energy calculations. The calculated surface phase diagrams are used to explain the experimental data and reveal that the stability of specific surface structures depends largely on the relative size of the surface constituents. Several structural models for the Ga-rich GaAs (001)(4×6) surface are discussed, but dismissed on energetic grounds. I discuss in some detail the electronic properties of the recently proposed cation-rich GaAs (001)ζ(4×2) geometry. Received: 18 May 2001 / Revised version: 23 July 2001 / Published online: 3 April 2002     

Adsorption of nonionic surfactant triton X-100 on solids from aqueous and nonaqueous solutions

The adsorption of nonionic surfactant Triton X-100 on quartz sand and methylated quartz sand from water and toluene was investigated by means of spectrophotometry, the radiotracer technique, and wetting angle measurements.     

Numerical analysis of time-dependent Boussinesq models

In this paper we analyse numerical models for time-dependent Boussinesq equations. These equations arise when so-called Boussinesq terms are introduced into the shallow water equations. We use the Boussinesq terms proposed by Katapodes and Dingemans. These terms generalize the constant depth terms given by Broer. The shallow water equations are discretized by using fourth-order finite difference formulae for the space derivatives and a fourth-order explicit time integrator. The effect on the stability and accuracy of various discrete Boussinesq terms is investigated. Numerical experiments are presented in the case of a fourth-order Runge-Kutta time integrator.     

A numerical study of time-dependent schr?dinger equation for multiphoton vibrational interaction of NO molecule, modelled as Morse oscillator, with intense far-infrared femtosecond lasers

For the NO molecule, modelled as a Morse oscillator, time-dependent (TD) nuclear Schr?dinger equation has been numerically solved for the multiphoton vibrational dynamics of the molecule under a far-infrared laser of wavelength 10503 nm, and four different intensities,I = 1 × 10⁸, 1 × 10¹³, 5 × 10¹⁶, and 5 × 10¹⁸ W cm⁻² respectively. Starting from the vibrational ground state at zero time, various TD quantities such as the norm, dissociation probability, potential energy curve and dipole moment are examined. Rich high-harmonics generation (HHG) spectra and above-threshold dissociation (ATD) spectra, due to the multiphoton interaction of vibrational motions with the laser field, and consequent elevation to the vibrational continuum, have been obtained and analysed. Dedicated to Professor C N R Rao on his 70th birthday An erratum to this article is available at .     

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007